Portable electronic devices, such as those configured to be handheld or otherwise associated with a user, are employed in a wide variety of applications and environments. Increasingly, such devices are equipped with one or more sensors or other systems for determining the position or motion of the portable device. Notably, devices such as smartphones, tablets, smart watches or other portable devices may feature low cost Micro-Electro-Mechanical Systems (MEMS) sensors, such as gyroscopes, accelerometers, magnetometers, and barometers. These sensors are small and lightweight, consume little power, and are extremely low-cost. By virtue of these advantages. MEMS sensors have become appropriate candidates for motion tracking and navigation applications. For consumer portable devices, inertial navigation systems (INS), and dead-reckoning such as pedestrian dead-reckoning (PDR) can be used to navigate with inertial sensors. PDR may be the algorithm used to navigate with inertial sensors in case of on-foot motion, such as walking or running, other dead-reckoning techniques can be used such as vehicular dead-reckoning (when speed of vehicle is measured) or cycling dead-reckoning (when periodic motion is detected). INS may also be used in vehicles or other vessels. Inertial sensors are not dependent on the transmission or reception of signals from an external source; thus, they are ideal for providing continuous information in indoor/outdoor environments.
However, inertia sensors provide only short-term accuracy and suffer from accuracy degradation over time. Although the horizontal attitude (i.e., roll and pitch) errors can be controlled by accelerometer measurements, the heading error typically grows when there is no aiding information. Furthermore, there is a misalignment issue in portable navigation application (such as for example pedestrian applications among others) because the orientation of mobile devices can keep changing relative to the movement of the platform or users body. To correct for the increasing errors, external technologies such as absolute navigational information, such as a Global Navigation Satellite System (GNSS) or magnetometers may be needed. Such technologies may not provide sufficient reliability. Specifically, typical GNSS signals are too weak to penetrate into indoor environments; also, there are significant multi-path effects in deep urban areas. Further, when using magnetometers, the local magnetic field is susceptible to interferences from man-made infrastructiues in indoor or urban environments, which makes magnetometer-derived heading angles unreliable.
As a result, multi-sensor integrated navigation performance may not meet the requirement of all applications, especially for portable navigation. Hence, other methods such as smoothing are required to enhance the navigation performance. Portable navigation where the device containing the sensors can move constrained or unconstrained with in a platform (user, vehicle, or vessel of any type), and where the orientation of the device can change freely with respect to the platform, and where the platform can go to any environment (even with no absolute navigational information available) presents a challenging conditions for existing smoothing techniques that may not be able to provide a desired level of performance. Thus, there is a need for more efficient smoothing techniques to be able to cope with all challenges, especially those of portable navigation. As will be described in the following materials, this disclosure satisfies these and other needs.